Apparatus and method for fast generation of three-dimensional (3d) hologram

ABSTRACT

An apparatus for generating a hologram that may generate a three-dimensional (3D) hologram pattern at a high speed may include a pattern setting unit to set points for which hologram patterns are to be generated with respect to a one-eighth area of an entire area for which a hologram pattern is to be generated, a calculation unit to calculate pattern values for a plurality of reference points selected with respect to the one-eighth area of the entire area, and to generate a pattern for the one-eighth area using recurrent interpolation, and a pattern duplicating unit to complete a pattern for the entire area by duplicating the generated pattern for the one-eighth area.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the priority benefit of Korean PatentApplication No. 10-2012-0007210, filed on Jan. 25, 2012, in the KoreanIntellectual Property Office, the disclosure of which is incorporatedherein by reference.

BACKGROUND

1. Field

The following description relates to an apparatus and method ofexpediting generation of a three-dimensional (3D) hologram, and moreparticularly, to a method and apparatus for generating a hologrampattern using an operational apparatus by receiving an input of data ofa spatial object or image data including color and depth.

2. Description of the Related Art

A stereoscopic image is provided to realize a three-dimensional (3D)image. However, since the stereoscopic image has a limit due to visualfatigue, a limited number of view points, and the like, a method ofrealizing a 3D image using a hologram is drawing attention.

A hologram is technology for representing a 3D space that has alimitless number of viewpoints and causes little visual fatigue byreproducing a 3D spatial object using a strength and phase of light.Generally, a hologram is generated using a computer generated hologram(CGH) in a method of generating a digital hologram. That is, in thedigital hologram generating method, optical signals are approximated,and a hologram is generated using an interference pattern generatedthrough a mathematical operation.

In the digital hologram generating method, a 3D spatial object isconstrued as a set of 3D points, and point holograms corresponding toall 3D points constituting the 3D spatial object are generated. In thisinstance, as the sophistication or complexity of the 3D spatial objectincreases so too does a number of 3D points included in the 3D spatialobject, and thus, an amount of calculation subsequently increases.

SUMMARY

According to example embodiments, an apparatus and method of generatinga hologram that may expedite generation of a three-dimensional (3D)hologram are disclosed.

According to example embodiments, an apparatus and method that mayexpedite generation of a 3D hologram, without relying on a separatelook-up table (LUT), are disclosed.

According to example embodiments, an apparatus and method of generatinga hologram that may be suitable for a parallel process using multipleprocessors, and may minimize an operational delay resulting fromexternal memory access, are disclosed.

The foregoing and/or other aspects are achieved by providing anapparatus for generating a hologram, the apparatus including acalculation unit to generate a pattern for a partial area by recurrentinterpolation using input 3D data, the partial area corresponding to aportion of an entire area for which a hologram pattern is to begenerated, and a pattern duplicating unit to complete a pattern for theentire area by duplicating the generated pattern for the partial area.

The partial area may correspond to a one-eighth area of the entire area.

The calculation unit may calculate Fresnel Zone Plate (FZP) patternvalues for a plurality of reference points in the partial area, and maycalculate FZP pattern values for points excluding the plurality ofreference points in the partial area, by performing interpolation usingan FZP pattern value calculated for at least one point, among theplurality of reference points.

In this instance, the calculation unit may calculate FZP pattern valuesfor the plurality of reference points, using a solution of a waveequation, for example, a Rayleigh-Sommerfeld solution.

The calculation unit may include a plurality of processors to performparallel recurrent interpolation, and the apparatus may further includea scheduling unit to perform scheduling for the parallel recurrentinterpolation with respect to the plurality of processors.

The apparatus may further include a pattern setting unit to select thepartial area from the entire area, and to determine a size of a patternin the partial area.

The foregoing and/or other aspects are achieved by providing anapparatus for generating a hologram, the apparatus including a patternsetting unit to set points at which a hologram pattern is to begenerated with respect to a one-eighth area of an entire area for whicha hologram pattern may be generated, and a calculation unit to calculatepattern values for a plurality of reference points selected in theone-eighth area of the entire area, and to generate a pattern for theone-eighth area by a recurrent interpolation scheme, based on thecalculated pattern values for the plurality of reference points.

In this instance, the apparatus may further include a patternduplicating unit to complete a pattern for the entire area byduplicating the generated pattern for the one-eighth area.

The calculation unit may calculate FZP pattern values for the pluralityof reference points, using a solution of a wave equation.

The calculation unit may include a plurality of processors to performparallel recurrent interpolation, and the apparatus may further includea scheduling unit to perform scheduling for the parallel recurrentinterpolation with respect to the plurality of processors.

The foregoing and/or other aspects are achieved by providing a method ofgenerating a hologram, the method include generating, by a calculationunit of a hologram generating apparatus, a pattern for a partial area byrecurrent interpolation using input 3D data, the partial areacorresponding to a portion of an entire area for which a hologrampattern is to be generated, and completing, by a pattern duplicatingunit of the hologram generating apparatus, a pattern for the entire areaby duplicating the generated pattern for the partial area.

Additional aspects of embodiments will be set forth in part in thedescription which follows and, in part, will be apparent from thedescription, or may be learned by practice of the disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

These and/or other aspects will become apparent and more readilyappreciated from the following description of embodiments, taken inconjunction with the accompanying drawings of which:

FIG. 1 illustrates an apparatus for generating a hologram according toexample embodiments;

FIG. 2 illustrates a process of generating a hologram according toexample embodiments;

FIG. 3 illustrates a calculating process of an apparatus for generatinga hologram according to example embodiments;

FIG. 4 illustrates a hologram pattern generated according to exampleembodiments;

FIG. 5 illustrates a process of generating a pattern according toexample embodiments;

FIGS. 6A and 6B illustrate reference points for which pattern values arepre-calculated in recurrent interpolation according to exampleembodiments;

FIG. 7 illustrates a process of calculating a pattern value at a pointaccording to example embodiments;

FIGS. 8 and 9A through 9D illustrate a process of recurrentinterpolation according to example embodiments;

FIG. 10 illustrates a process of generating a pattern for an entire areaby duplicating a pattern for a partial area according to exampleembodiments;

FIGS. 11A and 11B illustrate operational states of processors of FIG. 8according to example embodiments;

FIGS. 12A through 13C illustrate a process of recurrent interpolationperformed by a scheduling method, and operational states of processorsin the process according to example embodiments;

FIG. 14 illustrates a method of generating a hologram according toexample embodiments; and

FIG. 15 illustrates recurrent interpolation in a method of generating ahologram according to example embodiments.

DETAILED DESCRIPTION

Reference will now be made in detail to embodiments, examples of whichare illustrated in the accompanying drawings, wherein like referencenumerals refer to like elements throughout. Embodiments are describedbelow to explain the present disclosure by referring to the figures.

FIG. 1 illustrates an apparatus 100 for generating a hologram accordingto example embodiments.

When memory allocation and hologram initialization are performed, and 3Dpoint data is received by the apparatus 100, a process of generating athree-dimensional (3D) hologram image may be initiated.

A pattern setting unit 110 may set a size of a Fresnel Zone Plate (FZP)pattern, which is an interval of a point for which a pattern value maybe calculated, by determining a size of a pattern. A shape of thepattern and a size of the pattern will be further described withreference to FIGS. 2 through 6.

A calculation unit 130 may calculate pattern values for reference pointsin order to directly calculate a pattern value for a one-eighth area,and also may calculate pattern values for other points in the one-eightharea, using recurrent interpolation.

A scheduling unit 120 may perform scheduling to minimize a number ofidle processors and a number of processing iterations when processorsincluded in the calculation unit 130 calculate the pattern valuesthrough recurrent interpolation.

The scheduling process will be further described with reference to FIGS.11 through 13.

Through the aforementioned processes, the calculation unit 130 maycomplete the pattern for the one-eighth area, and a pattern duplicatingunit 140 may complete a pattern for the entire area by duplicating thecompleted pattern for the one-eighth area throughout the entire area.

The process of duplicating the pattern will be further described withreference to FIG. 10.

FIG. 2 illustrates a process of generating a hologram according toexample embodiments.

A hologram may refer to technology for restoring a 3D image identical toan original image, by recording and reproducing phase information andintensity of light, that is, an electromagnetic (EM) wave, in a space.

In a case of a computer generated hologram, a hologram pattern maygenerally be generated based on information about a 3D space and anobject, in order to directly capture phase information and intensity oflight, due to such difficulties as maintenance of darkroom environment,control of short-wavelength light, or management of movements of anobject, for example.

However, because intensity and phase information on a hologram plane mayneed to be calculated for all spatial points, a great amount of time maybe expended in generating a hologram. Typically, thousands to tens ofthousands of seconds are expended in generating a single piece of ahologram.

Example embodiments may expedite an operational process in the processof generating the hologram.

FIG. 3 illustrates a calculating process of an apparatus for generatinga hologram according to example embodiments.

According to example embodiments, a hologram pattern may be generatedusing a solution of a wave equation. For example, a 3D hologram may beobtained by generating a hologram pattern for a one-eighth areacorresponding to a portion of an entire area, using aRayleigh-Sommerfeld solution, hereinafter referred to as an R-Ssolution, as expressed by Equation 1, and generating a pattern for theentire area by duplicating the generated hologram pattern for theone-eighth area over the entire area.

In the process of generating the pattern for the one-eighth area,pattern values for only a portion of reference points may be calculated,and pattern values for other points excluding the reference points maybe calculated using recurrent interpolation.

Terms dp and k in Equation 1 may be defined as expressed by Equations 2and 3, respectively.

$\begin{matrix}{d_{p} = {\sqrt{\left( {\xi - x_{p}} \right)^{2}} + \left( {\eta - y_{p}} \right) + z_{p}^{2}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack \\{k = \frac{2\pi}{\lambda}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

The R-S solution may be approximated using binominal expansion asfollows.

In particular, if Equation 4 is true, then d_(p) may be calculated byEquation 5.

$\begin{matrix}{\rho^{2} = {\left( {\xi - x_{p}} \right)^{2} + {\left( {\eta - y_{p}} \right)^{2}\mspace{14mu} \left( {{from}\mspace{14mu} {Equation}\mspace{14mu} 2} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack \\\begin{matrix}{d_{p} = \sqrt{\rho^{2} + z_{p}^{2}}} \\{= {z_{p}\sqrt{\begin{pmatrix}\rho \\z_{p}\end{pmatrix}^{2} + 1}}} \\{\approx {z_{p}\left( {1 + \begin{matrix}\rho^{2} \\{2z_{\rho}^{2}}\end{matrix}} \right)}} \\{= {z_{p} + \frac{\rho^{2}}{2\; z_{p}}}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

Accordingly, an approximation of the R-S solution may be expressed byEquation 6.

FIG. 4 illustrates a hologram pattern 400 generated according to exampleembodiments.

As can be understood from the hologram pattern 400 for an entire areaand the approximation of Equation 6, a hologram pattern to be generatedat portions that are located a predetermined distance away from apredetermined point may be concentrically symmetric. Accordingly, inview of concentric symmetry elimination, an FZP pattern for only aone-eighth area may be generated without generating all patterns for theentire area one by one, and the generated pattern for the one-eightharea may be duplicated for remaining areas, whereby a pattern for theentire area may be obtained.

That is, when the concentric symmetry of the hologram pattern is used,pattern values for one-dimensional (1D) points may be calculateddirectly through ρ=√{square root over ((ξ−x_(p))²+(η−y_(p))²)}{squareroot over ((ξ−x_(p))²+(η−y_(p))²)} of Equation 2, and patterns for otherpoints corresponding to (ξ, η) may be obtained indirectly by using thepre-calculated pattern values.

FIG. 5 illustrates a conceptual diagram 500 to describe a process ofgenerating a pattern according to example embodiments.

As aforementioned, when an FZP pattern for a one-eighth area 510 isgenerated, an FZP pattern for a quarter area as shown in the conceptualdiagram 500 may be generated by duplicating the generated FZP patternfor the one-eighth area 510. By iteratively duplicating the generatedFZP pattern for the quarter area, an FZP pattern for an entire area maybe generated.

When the FZP pattern is generated for the one-eighth area 510, patternsfor only points present on a 1D line in a single predetermined directionmay be generated, without generating patterns for all points in theone-eighth area 510, and the FZP pattern for the one-eighth area 510 maybe generated through recurrent interpolation.

In this instance, a look-up table (LUT) containing a correlation between1D pattern data and radius data may be used.

A value ρ according to the radius data may be pre-calculated in the LUT,and patterns for uncalculated portions may be determined directly byreferring to the LUT table, based on calculations performed with respectto the 1D pattern data.

However, when a resolution of a hologram to be displayed increases, asize of the LUT may increase, an amount of time required for externalmemory access may increase, and a large amount of data may need to bestored in a global memory. Accordingly, a plurality of processors mayexperience difficulty in performing parallel processes.

Thus, according to example embodiments, a hologram pattern for theone-eighth area 510 may be generated by directly calculating only 1Dpattern data, without using an LUT of radius data, and rapidlycalculating data for other portions through recurrent interpolation.

FIGS. 6A and 6B illustrate reference points for which pattern values arepre-calculated according to example embodiments.

For ease of description, it may be assumed that x_(p)=0, y_(p)=0 incoordinates (x_(p), y_(p)) of a point corresponding to the center of apattern having concentric symmetry. The assumption may not beproblematic since relative coordinates and absolute coordinates may bereadily interchangeable.

A pattern value at the origin corresponding to x_(p)=0, y_(p)=0 may becalculated based on Equation 6, as expressed by Equation 7.

In Equation 7, a value in

(the dashed box) may be referred to as a variable phase distance (VPD).According to the aforementioned concentric symmetry, when the VPD isidentical, a pattern may have an identical phase on a holographic plane.

Although an R-S solution may be calculated along a diagonal line, theR-S solution may not necessarily be calculated along the diagonal line.Instead, initial R-S solutions may be calculated for points on asuitable 1D line, or a portion of predetermined reference points,depending on applications.

The calculating process may be performed in real time using thecalculated initial values for the reference points. Depending on exampleembodiments, the calculated initial values may be used as an LUT.

Among the reference points of FIGS. 6A and 6B, namely, solid blackpoints corresponding to points for which pattern values are calculated,let a position of a reference point at (nδ_(ξ), mδ_(η)) be A, a positionof a reference point at ((n−1)δ_(ξ)(m−1)δ_(η)) be B, and a position of areference point at ((m−1)δ_(ξ), nδ_(q)) be P. A VPD at each position maybe calculated as expressed by Equations 8 through 10, respectively.

$\begin{matrix}{d_{m,n} = \frac{\left( {m\; \delta_{\xi}} \right)^{2} + \left( {n\; \delta_{\eta}} \right)^{2}}{2\; z_{p}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack \\{d_{{m - 1},{n - 1}} = \begin{matrix}{\left( {\left( {m - 1} \right)\delta_{\xi}} \right)^{2} + \left( {\left( {n - 1} \right)\delta_{\eta}} \right)^{2}} \\{2\; z_{p}}\end{matrix}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack \\{d_{{m - 1},n} = \begin{matrix}{\left( {\left( {m - 1} \right)\delta_{\xi}} \right)^{2} + \left( {n\; \delta_{\eta}} \right)^{2}} \\{2\; z_{p}}\end{matrix}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

FIG. 7 illustrates a process of calculating a pattern value at a pointaccording to example embodiments.

In the abovementioned equations, when Q is a point that is distant fromthe origin by d_(m-1,n), and positioned on a line AB, Equations 11 and12 may be completed with respect to m,n≧1

$\begin{matrix}{a = {{\overset{\rightarrow}{AQ}} = {{d_{{m - 1},n} - d_{{m - 1},{n - 1}}} = \frac{\left( {{2n} - 1} \right)\delta_{\eta}^{2}}{2\; z_{p}}}}} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack \\{b = {{\overset{\rightarrow}{QB}} = {{d_{m,n} - d_{{m - 1},n}} = \frac{\left( {{2m} - 1} \right)\delta_{\xi}^{2}}{2\; z_{p}}}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

Also, let a hologram pattern value at a point A be V(m−1, n−1), and ahologram pattern value at a point B be V(m, n). A hologram pattern valueV(m−1, n) at a point P which is yet to be calculated may be calculatedby linear interpolation, as expressed by Equation 13.

                                     [Equation  13] $\begin{matrix}{{V\left( {{m - 1},n} \right)} = \underset{\frac{{({{2m} - 1})}\delta_{\xi}^{2}}{2\; z_{p}} + \frac{2{({n - 1})}\delta_{\eta}^{2}}{2z_{p}}}{{\begin{matrix}{\left( {{2m} - 1} \right)\delta_{\xi}^{2}} \\{2\; z_{p}}\end{matrix}{V\left( {{m - 1},{n - 1}} \right)}} + {\begin{matrix}{\left( {{2n} - 1} \right)\delta_{\eta}^{2}} \\{2\; z_{p}}\end{matrix}{V\left( {m,n} \right)}}}} \\{= \underset{{{({{2m} - 1})}\delta_{\xi}^{2}} + {2{({n - 1})}\delta_{\eta}^{2}}}{{\left( {{2m} - 1} \right)\delta_{\xi}^{2}{V\left( {{m - 1},{n - 1}} \right)}} + {\left( {{2n} - 1} \right)\delta_{\eta}^{2}{V\left( {m,n} \right)}}}}\end{matrix}$

A process of performing the aforementioned process iteratively, usingpoints for which pattern values are pre-calculated with respect topoints for which pattern values are yet to be calculated, may correspondto recurrent interpolation that is mentioned throughout the presentdisclosure.

The above described process may be performed in parallel by processorsincluded in the calculation unit 130 of FIG. 1, which will be describedin detail later.

FIGS. 8 and 9A through 9D illustrate a process of recurrentinterpolation according to example embodiments.

As shown in FIG. 8, V(m−1, n) may be obtained from V(m, n) and V(m−1,n−1), with respect to predetermined values of m and n, and patternvalues for points included in a one-eighth area may be calculatedthrough Iteration 1 of FIG. 9A, Iteration 2 of FIG. 9B, Iteration 3 ofFIG. 9C, and Iteration 4 of FIG. 9D.

Although linear interpolation is used as an example for ease ofdescription, it may be possible to recurrently perform higher orderinterpolation to obtain a more accurate hologram pattern value. Inaddition, it will be understood that various changes in form and detailsmay be made therein without departing from the spirit and scope of thepresent disclosure.

FIG. 10 illustrates a process of generating a pattern for an entire areaby duplicating a pattern for a partial area of the entire area accordingto example embodiments.

The pattern duplicating unit 140 of FIG. 1 may duplicate a pattern for aone-eighth area 1001 generated by the calculation unit 130 to aneighboring one-eighth area 1002 for which a pattern is yet to begenerated, by recurrent interpolation.

A pattern for a quarter area 1010 may be completed, and the patternduplicating unit 140 may duplicate the pattern for the quarter area 1010to another neighboring quarter area 1020.

By iterating the process, the pattern duplicating unit 140 may completepatterns for other quarter areas 1030 and 1040, and may complete apattern 1000 for an entire area.

FIGS. 11A and 11B illustrate operational states of processors of FIG. 8according to example embodiments.

A process of generating patterns for all points in a one-eighth area maybe performed by sequential computation of one processor included in thecalculation unit 130 of FIG. 1.

However, the process of generating the patterns for all points in theone-eighth area may be performed by parallel computation of a pluralityof processors included in the calculation unit 130.

FIG. 11A illustrates a process of performing recurrent interpolationcomputing in parallel by a plurality of processors, for example, Proc #1through Proc #9. FIG. 11B illustrates operational states of theplurality of processors while the process of FIG. 11A is performed.

Because a number of idle processors may increase as the iterations areperformed iteratively in the parallel process, improvement in efficiencymay be demanded.

According to other example embodiments, separate scheduling may beperformed to increase a computing rate by reducing a number of idleprocessors.

FIGS. 12A through 13C illustrate a process of recurrent interpolationperformed by a scheduling method, and operational states of processorsin the process according to example embodiments.

The scheduling unit 120 of FIG. 1 may set points for which patternvalues may be pre-calculated, as shown in FIG. 12A.

When the iterations are performed, recurrent interpolation may beallocated to processors, for example, Proc #1 through Proc #9, as shownin FIGS. 12B through 12D, and FIGS. 13A and 13B.

Operational states of the processors may be shown in FIG. 13C.

When compared to the operational states of FIG. 11B, it may beunderstood that a number of idle processors is remarkably reduced, andan overall number of iterations performed is reduced as well.

FIG. 14 illustrates a method of generating a hologram according toexample embodiments.

In operation 1410, a process of generating a 3D hologram image may beinitiated, and memory allocation and hologram initialization may beperformed.

In operation 1420, the apparatus 100 of FIG. 1 for generating a hologrammay generate a hologram using 3D point data when the 3D point data isreceived.

In operation 1430, the pattern setting unit 110 of FIG. 1 may determinea size of an FZP pattern, which is an interval of a point for which apattern value is to be actually calculated, and the like.

In operation 1440, the calculation unit 130 of FIG. 1 may calculatepattern values for reference points to calculate the pattern valuesdirectly.

In operation 1450, the calculation unit 130 may generate an FZP patternin a one-eighth area using recurrent interpolation. The calculationprocess performed by the recurrent interpolation may be identical to thedescription provided with reference to FIGS. 6 through 9. The recurrentinterpolation will be described later based on a flowchart of FIG. 15.

In operation 1460, the pattern duplicating unit 140 may duplicate theFZP pattern for the one-eighth area that is generated by the calculationunit 130, whereby patterns for other one-eighth areas or patterns forother quarter areas may be completed. This process may be identical tothe description provided with reference to FIG. 10 and thus, aduplicated description will be omitted for conciseness.

In operation 1470, the FZP patterns generated thus far may be added as ahologram pattern. Whether an additional hologram pattern is to begenerated may be determined in operation 1480, and the process ofoperations 1420 through 1470 may be iterated, as necessary.

FIG. 15 illustrates recurrent interpolation in a method of generating ahologram according to example embodiments.

In operation 1510, a size of an FZP pattern may be determined by thepattern setting unit 110 of FIG. 1. In this process, a pixel pitchregarding how precisely a pattern is to be generated may be determined.

In operation 1520, memory allocation and FZP pattern initialization maybe performed. A process of calculating pattern values for referencepoints in operation 1530 may be similar to the flowchart of FIG. 14.

In operations 1540 through 1580, pattern values may be calculated forpoints, which neighbor the reference points and for which pattern valuesare yet to be calculated, through recurrent interpolation, bysequentially increasing a number of iterations.

When the iterations are terminated, the calculated pattern values may bestored in operation 1590, and a process of generating a pattern for anentire area may be performed by the pattern duplicating unit 140 of FIG.1.

The method according to the above-described embodiments may be recordedin non-transitory computer-readable media including program instructionsto implement various operations embodied by a computer. The media mayalso include, alone or in combination with the program instructions,data files, data structures, and the like. The program instructionsrecorded on the media may be those specially designed and constructedfor the purposes of embodiments, or they may be of the kind well-knownand available to those having skill in the computer software arts.Examples of non-transitory computer-readable media include magneticmedia such as hard disks, floppy disks, and magnetic tape; optical mediasuch as CD ROM discs and DVDs; magneto-optical media such as opticaldiscs; and hardware devices that are specially configured to store andperform program instructions, such as read-only memory (ROM), randomaccess memory (RAM), flash memory, and the like. The computer-readablemedia may also be a distributed network, so that the programinstructions are stored and executed in a distributed fashion. Theprogram instructions may be executed by one or more processors. Thecomputer-readable media may also be embodied in at least one applicationspecific integrated circuit (ASIC) or Field Programmable Gate Array(FPGA), which executes (processes like a processor) programinstructions. Examples of program instructions include both machinecode, such as produced by a compiler, and files containing higher levelcode that may be executed by the computer using an interpreter. Thedescribed hardware devices may be configured to act as one or moresoftware modules in order to perform the operations of theabove-described embodiments, or vice versa.

Although embodiments have been shown and described, it would beappreciated by those skilled in the art that changes may be made inthese embodiments without departing from the principles and spirit ofthe disclosure, the scope of which is defined by the claims and theirequivalents.

What is claimed is:
 1. An apparatus for generating a hologram, theapparatus comprising: a calculation unit to generate a pattern for apartial area by recurrent interpolation using input three-dimensional(3D) data, the partial area corresponding to a portion of an entire areafor which a hologram pattern is to be generated; and a patternduplicating unit to complete a pattern for the entire area byduplicating the generated pattern for the partial area.
 2. The apparatusof claim 1, wherein the partial area corresponds to a one-eighth area ofthe entire area.
 3. The apparatus of claim 1, wherein the calculationunit calculates Fresnel Zone Plate (FZP) pattern values for a pluralityof reference points in the partial area, and calculates FZP patternvalues for points excluding the plurality of reference points in thepartial area, by performing interpolation using an FZP pattern valuecalculated for at least one point, among the plurality of referencepoints.
 4. The apparatus of claim 3, wherein the calculation unitcalculates FZP pattern values for the plurality of reference points,using a solution of a wave equation.
 5. The apparatus of claim 1,wherein the calculation unit comprises a plurality of processors toperform parallel recurrent interpolation, and the apparatus furthercomprises a scheduling unit to perform scheduling for the parallelrecurrent interpolation with respect to the plurality of processors. 6.The apparatus of claim 1, further comprising: a pattern setting unit toselect the partial area from the entire area, and to determine a size ofa pattern in the partial area.
 7. An apparatus for generating ahologram, the apparatus comprising: a pattern setting unit to set pointsat which a hologram pattern is to be generated with respect to aone-eighth area of an entire area for which a hologram pattern isgenerated; and a calculation unit to calculate pattern values for aplurality of reference points selected in the one-eighth area of theentire area, and to generate a pattern for the one-eighth area by arecurrent interpolation scheme, based on the calculated pattern valuesfor the plurality of reference points.
 8. The apparatus of claim 7,further comprising: a pattern duplicating unit to complete a pattern forthe entire area by duplicating the generated pattern for the one-eightharea.
 9. The apparatus of claim 7, wherein the calculation unitcalculates Fresnel Zone Plate (FZP) pattern values for the plurality ofreference points, using a solution of a wave equation.
 10. The apparatusof claim 7, wherein the calculation unit comprises a plurality ofprocessors to perform parallel recurrent interpolation, and theapparatus further comprises a scheduling unit to perform scheduling forthe parallel recurrent interpolation with respect to the plurality ofprocessors.
 11. A method of generating a hologram, the methodcomprising: generating, by a calculation unit of a hologram generatingapparatus, a pattern for a partial area by recurrent interpolation usinginput three-dimensional (3D) data, the partial area corresponding to aportion of an entire area for which a hologram pattern is to begenerated; and completing, by a pattern duplicating unit of the hologramgenerating apparatus, a pattern for the entire area by duplicating thegenerated pattern for the partial area.
 12. The method of claim 11,wherein the generating of the pattern comprises calculating Fresnel ZonePlate (FZP) pattern values for a plurality of reference points in thepartial area, and calculating FZP pattern values for points excludingthe plurality of reference points in the partial area, by performinginterpolation using an FZP pattern value calculated for at least onepoint, among the plurality of reference points.
 13. The method of claim12, wherein the generating of the pattern comprises calculating FZPpattern values for the plurality of reference points, using a solutionof a wave equation.
 14. The method of claim 11, further comprising:performing, by a scheduling unit of the hologram generating apparatus,scheduling for parallel recurrent interpolation with respect to aplurality of processors included in the calculation unit.
 15. Anon-transitory computer-readable medium comprising a program forinstructing a computer to perform a method of generating a hologram,wherein the method comprises: generating, by a calculation unit of ahologram generating apparatus, a pattern for a partial area by recurrentinterpolation using input three-dimensional (3D) data, the partial areacorresponding to a portion of an entire area for which a hologrampattern is to be generated; and completing, by a pattern duplicatingunit of the hologram generating apparatus, a pattern for the entire areaby duplicating the generated pattern for the partial area.
 16. Theapparatus of claim 1, wherein the recurrent interpolation comprisesgenerating the pattern iteratively, using points for which patternvalues are pre-calculated with respect to points for which patternvalues are yet to be calculated.
 17. The apparatus of claim 1, whereinthe generation of a pattern for a partial area comprises using aRayleigh-Sommerfeld solution.
 18. The apparatus of claim 3, wherein thecalculation unit calculates FZP pattern values for points present on a1-dimensional line in a single predetermined direction.